After two scoreless periods that saw both teams miss a number of chances, Canada pulled in front when Meghan Agosta-Marciano ripped a shot past Finnish goalie Noora Raty on the powerplay with just over 10 minutes to play.
Jayna Hefford added another goal with a dazzling deke on Raty three minutes later and Rebecca Johnston tallied finished it off with a two-on-one break.
"We knew that Finland was going to come out and bring it. They are an unbelievable team, they have improved so much and we knew we needed to be patient," Agosta-Marciano told reporters.
"We didn't get frustrated, we stuck to the game plan, we kept coming, we kept getting shots on net and sooner or later once we got that one, we got three."
The win extended Canada's impressive streak of never losing a game in a major ice hockey competition to any other nation than the United States.
They play their neighbours in their final preliminary group game on Wednesday but, with both teams already safely assured a quarter-final bye, there is only pride, and the chance to gain a psychological edge ahead of their expected return meeting in the gold medal game, at stake.
Raty, who made 40 saves in her team's 3-1 loss to the United States on Saturday, baffled Canada's shooters for much of the game and turned aside 39 shots in another strong showing.
"We played really well for 50 minutes and then the last 10 minutes we ran into penalty trouble and that takes a lot of energy out of our players, including myself. So we kind of ran out of gas there," she said.
"We were close but is wasn't enough. We played well but if you want to beat the U.S. or Canada you have to play a full 60 minutes."
Finland will close out the preliminary round on Wednesday against Switzerland, with both teams moving to the quarter-finals to play the top two teams from Group B.